Estimation Of Single-index Quantile Model With Discrete Explanatory Variables

In recent years,the semiparametric regression model with index terms is one of the most important models in the high-dimensional semiparametric statistical model.Whether it is theoretical research or solving practical problems,it is the research hotspot of the majority of scholars.It mainly includes single index model,partial single index model,single index variable coefficient model and variable coefficient single index model,etc.it can effectively avoid "curse of dimensionality" and solve high-dimensional problems by transforming high-dimensional data into single index variables through dimension reduction technology.It has the flexibility of nonparametric model and can reflect the impact well on the premise of good interpretability the relationship between strain and high dimensional explanatory variables.Nowadays,nonparametric model estimation methods are mainly based on likelihood method,least square method and section likelihood method,but when there are outliers or random errors are not normal distribution,model estimation accuracy will be greatly reduced.At the same time,mean regression can only describe the average level of response variables,while quantile regression can describe the distribution of response variables more carefully,provide more information,and avoid the influence of outliers on the model results.In addition,the existing models rarely study discrete explanatory variables,which has some defects in solving practical problems.Therefore,this paper studies the single index quantile model with discrete explanatory variables and its estimation by combining the semiparametric model and quantile model.In order to get the overall robust coefficient estimation,this article will introduce an iterative estimation method of the single index quantile model with discrete explanatory variables.From previous studies,the quantile estimation is usually based on minimizing the sum of quantile loss functions to get the estimation of coefficients and connection functions,but the model in this paper contains discrete explanatory variables,which makes the estimation process complicated.Therefore,in this article,a new set of discrete explanatory variables is constructed by combining the direct method of discrete explanatory variables in single index model.First,the continuous explanatory variables are estimated by the weighted derivative method when z?S2 given,then the coefficients of discrete explanatory variables are estimated by combining the direct estimation method proposed by Horowitz and hardle(1996).Finally,the link function is estimated by the method of local linear quantile regression Make an estimate.Under certain conditions,this article selects the four quantiles of 0.1,0.3,0.5,and 0.7,and the effectiveness of this method in small sample estimation is illustrated by simulation experiments,and the advantages of this method in practical modeling are verified by case analysis.